1. Field of the Invention
The present invention relates to a position calculating method of calculating the position of a position-detected object, on the basis of the detected signal waveform which is obtained by detecting an alignment mark attached to the position-detected object, for use in detecting the position of the position-detected object such as a wafer or the like, for example, in such a photolithographic device as to expose a photoresist in lithography performed during the manufacturing process of a semiconductor device.
2. Description of the Related Art
It is necessary to calculate the accurate position of a semiconductor wafer for the accurate light exposure of a photoresist on the semiconductor wafer, in the technique such as lithography performed during the manufacturing process of a semiconductor device. A slice method, by way of example, is used for describing the conventional calculating method of calculating the position of a semiconductor wafer by detecting an alignment mark attached to a semiconductor wafer.
FIG. 6 shows a scanning waveform and a calculated parameter obtained by the method of detecting an edge scattered light after a laser beam is applied to the alignment mark attached to the semiconductor wafer. FIG. 7 is a flow chart showing an operation of detecting the position of a semiconductor wafer by the use of the conventional slice method.
In FIG. 6, S designates a specified slice level for use in calculating a medial point, A designates an intersection (on the left side) of the specified slice level and the slope, B designates an intersection (on the right side) of the specified slice level and the slope, C designates a mark detecting position (a medial point of A and B), X designates a slope rising point of a signal waveform (on the left side), Y designates a slope rising point of a signal waveform (on the right side), Z designates the accurate position of the alignment mark (a medial point of X and Y), E designates a positioning deviation, .theta.1 designates the angle of the slope of the signal waveform (on the left side), and .theta.2 designates the angle of the slope of the signal waveform (on the right side).
First of all, smoothing processing is performed on the signal waveform obtained on the basis of the signal intensity of the edge scattered light of the laser beam detected correspondingly to the position on the wafer stage (Step 701). The points A and B on the both sides of the slope of the signal waveform at the slice level S are required assuming that the minimum value of the signal intensity is defined as 0%, and the maximum value thereof is defined as 100% (Step 702). The slice level S may be a level specified beforehand or it may be decided on the basis of the maximum value of the first differential component of the signal waveform slope within the predetermined slice level area. At last, the medial point C of the segment AB is computed, and the position of the point C is obtained as the position for an alignment mark (Step 703).
The detecting processing of an alignment mark by the above-mentioned conventional slice method, has such a defect that a deviation occurs between the correct position of the alignment mark and the detected position thereof when the angles .theta.1 and .theta.2 on the both sides of the slope of the signal waveform differ from each other. Why it occurs will be described as follows.
The deviation between the angles .theta.1 and .theta.2 on the both sides of the slope of the signal waveform occurs when the angles of reflection of the light applied to the alignment mark differ between the facing edges of the mark pattern caused by the asymmetrical in the coating state of oxide, nitride, aluminum film or the like and the asymmetrical application state of a photoresist layered on the alignment mark. This asymmetrical phenomenon in the coating state of the film and the application state of the photoresist generally happens point-symmetrically with respect to the center of a wafer and its vicinities. Therefore, the sloping angle of the signal waveform shows a symmetrical characteristic with respect to the center of a wafer.
The correct position of the alignment mark is to stand in the center of the slope-rising areas of the signal waveform. More specifically, assuming that the points reflecting the correct positions of the edges for the alignment mark are defined as X and Y, the correct position of the alignment mark is indicated by the medial point Z of the segment XY in reference to FIG. 6. However, if there is a difference between the angles .theta.1 and .theta.2 as illustrated in FIG. 6, the higher the slice level becomes, the calculated position C is increasingly deviated from the correct mark position Z under the influence of the difference between the angles .theta.1 and .theta.2, thereby increasing the positioning deviation .epsilon..
While, the slope of the signal waveform has a more unstable shape according as the signal intensity is nearing the base level (0%), so that the slice level must be generally set at 20% or 30% and the more. Therefore, occurrence of the positioning deviation .epsilon. is further inevitable in addition to the above-mentioned cause of the positioning deviation .epsilon..
The above example has been described in case of the positional detection of a semiconductor wafer by a photolithographic device for exposing a photoresist on the semiconductor wafer to light. However, it is needless to say that the same things happen generally in the various devices for detecting the position of a position-detected object through the analysis of the signal waveform obtained by detecting the reflected scattered light of a laser beam.